"Electron-phonon coupling underpins some of the most important states of matter (such as superconductivity and ferroelectricity) and is notoriously difficult to control," explains team member Avishai Benyamini. “In nature, this coupling is predetermined by the parameters of a given material and can only be modified slightly. On the other hand, in our nanotube devices we can control both mechanical and electronic properties, something that allows us to modify the electron-phonon coupling at will.”

The researchers made their devices from small-bandgap carbon nanotubes suspended between pairs of metallic contacts above a series of gate electrodes. By tuning the voltages on these gates, they were able to create potential wells (or quantum dots) for electrons at different positions along the nanotube, which allowed them to choose exactly where the electrons were confined.

“This control over the electrostatic potential is key for engineering the forces acting on the electrons and consequently their coupling to the mechanical motion of the suspended nanotube,” explains Benyamini. “By varying the locations of the electrons with gate voltages, we shape the electrostatic forces that act on the mechanical resonator.”

When an electron is confined to a specific position along the tube above a gate, an electrostatic force pulls it downwards towards this gate, pulling the entire nanotube along with it, just like a ball on a spring pulled by gravity towards the ground, he continues. “However, unlike the force of gravity, where the pull on the ball is not linked to its height, in our nanotube devices the electron is pulled more strongly the closer it is to the gate. This force gradient acts in the opposite direction to the elastic restoring force of the suspended nanotube, so effectively behaving as an 'anti-spring' that tries to push the ball away from its equilibrium position. This mechanism softens the overall spring constant of the system and is a direct manifestation of the coupling between the electronic and mechanical forces at play."

Switching coupling on and off

This coupling is analogous to the electron-phonon coupling in more conventional solids but with the added feature that the researchers can engineer where the field gradients are located, and thus tailor electron coupling to the mechanical motion of the resonator. "For example, we can switch off this coupling by confining the electrons to a position where the nanotube no longer vibrates – so that it is at the so-called nodal point of the phonon's wavefunction. However, if we place the electrons at a position where the nanotubes vibrates at its maximum (or at its antinode), the coupling between electrons and phonons will be strongest,” Benyamini told nanotechweb.org.

The technique provides a new way to manipulate mechanical systems both classically and quantum mechanically, he added. “Electron-phonon interactions are crucial in a variety of fundamental solid-state phenomena and being able to tune them should prove useful for studying condensed matter states such as ferroelectricity, Peierls and Jahn-Teller instabilities, and superconductivity in engineered environments not found in nature.”

The research is detailed in Nature Physics doi:10.1038/nphys2842.

Further reading

A piano for electrons in a carbon nanotube (Sep 2013)
Putting a new spin on nanotubes (Mar 2008)
New nanotube SET images buried crystal domains (Nov 2013)
Wigner molecule appears in carbon nanotube (Aug 2013)